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Source Condition Double Robust Inference on Functionals of Inverse Problems

Andrew Bennett, Nathan Kallus, Xiaojie Mao, Whitney Newey, Vasilis Syrgkanis, Masatoshi Uehara

arXiv 25 Jul 2023 · Statistics — Methodology · 1 citations (OpenAlex)

arXiv:2307.13793 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We consider estimation of parameters defined as linear functionals of solutions to linear inverse problems. Any such parameter admits a doubly robust representation that depends on the solution to a dual linear inverse problem, where the dual solution can be thought as a generalization of the inverse propensity function. We provide the first source condition double robust inference method that ensures asymptotic normality around the parameter of interest as long as either the primal or the dual inverse problem is sufficiently well-posed, without knowledge of which inverse problem is the more well-posed one. Our result is enabled by novel guarantees for iterated Tikhonov regularized adversarial estimators for linear inverse problems, over general hypothesis spaces, which are developments of independent interest.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1N. Dikkala, G. Lewis, L. Mackey, and V. Syrgkanis (2020) Minimax estimation of conditional moment models1.00095100%
2L. Liao, Y.-L. Chen, Z. Yang, B. Dai, M. Kolar, and Z. Wang (2020) Provably efficient neural estimation of structural equation models: An adversarial approach1.00094100%
3A. Bennett, N. Kallus, X. Mao, W. Newey, V. Syrgkanis, and M. Uehara (2023) Minimax instrumental variable regression and $ l_2 $ convergence guarantees without identification or closedness1.00073100%
4M. J. Wainwright (2019) High-dimensional statistics: A non-asymptotic viewpoint, volume 480.92843100%
5A. Bennett, N. Kallus, X. Mao, W. Newey, V. Syrgkanis, and M. Uehara (2022) Inference on strongly identified functionals of weakly identified functions0.874112100%
6L. Cavalier (2011) Inverse problems in statistics0.8435560%
7V. Chernozhukov, D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, an… (2017) Double/debiased/neyman machine learning of treatment effects0.84333100%
8M. Carrasco, j.-p. Florens, and E. Renault (2007) Chapter 77 linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization0.73732100%
9M. Carrasco, J.-P. Florens, and E. Renault (2007) Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization0.73732100%
10Y. Cui, H. Pu, X. Shi, W. Miao, and E. T. Tchetgen (2020) Semiparametric proximal causal inference0.73732100%

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